Nonlinear chaotic dynamics of arterial blood pressure and renal blood flow

Abstract

To determine whether arterial pressure (AP) and renal blood flow (RBF) are nonlinear dynamic processes (chaotic), we measured resting AP and RBF over 4 h in six conscious dogs. A catheter was placed in the aorta, and transit-time flowmeters were positioned around the renal artery. The average AP was 102 +/- 3 mmHg, and the mean RBF was 318 +/- 42 ml/min. We applied four analytic procedures to test the nature of AP and RBF time series, i.e., to determine if these variables are controlled randomly, if they consist of periodic oscillations, or whether they are best characterized as nonlinear dynamic processes. To this end, a fast Fourier transform was performed to quantify the amount of distinct periodic oscillations and nonperiodic variability in the very low frequency domain (< 0.01 Hz). The power spectrum of AP and RBF revealed broad band noise with no distinct peaks, which is commonly referred to as “1/f noise.” As a second procedure, time-delayed phase return maps were constructed, and as a third approach the correlation dimensions were estimated via the Grassberger-Procaccia algorithm. The correlation dimensions of RBF and AP were similar (RBF 3.3 +/- 0.37 vs. AP 3.6 +/- 0.23; P = 0.2). The fourth method determined sensitive dependence on initial conditions, a hallmark of nonlinear “chaotic” dynamics. We determined the maximal Lyapunov exponents and found them to be positive for AP (0.1 +/- 0.01) and for RBF (0.04 +/- 0.01) indicating that they both are nonlinear dynamic processes.(ABSTRACT TRUNCATED AT 250 WORDS)